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A Defense of Temperate Epistemic Transparency

A Defense of Temperate Epistemic Transparency. ELEONORA CRESTO CONICET (Argentina) University of Konstanz – July 2011. EPISTEMIC TRANSPARENCY. If S knows that p , S knows that she knows that p : KK Principle : Kp  KKp Knowledge reflexivity Positive introspection

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A Defense of Temperate Epistemic Transparency

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  1. A Defense of TemperateEpistemicTransparency ELEONORA CRESTO CONICET (Argentina) University of Konstanz – July 2011

  2. EPISTEMIC TRANSPARENCY • IfSknowsthatp, S knowsthatsheknowsthatp: • KK Principle: KpKKp • Knowledgereflexivity • Positive introspection • Self-knowledge • Transparency • Luminosity

  3. GOAL • A defense of a moderateversion of KK

  4. RISE AND FALL OF KK • 1960 s: Dogma Then…. • Externalism – e.g.: Reliabilism • Williamson (2000)

  5. STRATEGY • (A) Why do wewanttransparency? • (B) Indirectargument

  6. WHY DO WE CARE ABOUT TRANSPARENCY? • Ideal agents • Ideallyrational?

  7. WHY DO WE CARE ABOUT TRANSPARENCY? • Knowledge and responsibility • How?

  8. WHY DO WE CARE ABOUT TRANSPARENCY? • Responsibilitydemandsustobe in anappropriatereflectivestate. • Whatreflectivestate? • Epistemicresponsibilityentails “ratifiability”.

  9. A MODAL FRAME • F= <W, R, Pprior> • K = {w W: x W (wRxx )} • R(w) = {x W: wRx}

  10. WILLIAMSON: IMPROBABLE KNOWING • Pw(): theevidentialprobability of  in w. • Pw() = Pprior( | R(w)) = Pprior (R(w)) / Pprior(R(w)) • Pw(R(w)) = 1 • [P() = r] =def. {w W: Pw() = r}

  11. IMPROBABLE KNOWING • “The KK principle is equivalent to the principle that if the evidential probability of p is 1, then the evidential probability that the evidential probability of p is 1 is itself 1” (Williamson, p. 8). • We can build a model in whichPw([P(R(w))=1])is as low as wewant.

  12. PROBLEMS  Whyshouldwesaythattheevidentialbasis (in w) isalwaysR(w)?

  13. PROBLEMS Recallthat: • [P() = r] = {w W: Pw() = r} • [Pw() = r] ?

  14. PROPOSAL (FIRST VERSION) • We’llhave a sequence of languagesL0, L1, … Ln….withprobabilityoperatorsP0, …Pn… • We’llhave a sequence of functionsP1w…Pnw… onsentencesi of languageLi • Piw: Li-1 ℝ

  15. PROPOSAL (FIRST VERSION) • Expressions of the form Pprior() or Piw() do not belong to any language of the sequence L0, L1…Ln…. • “Pi()=r”is true in wiffPiw()=r.

  16. PROPOSAL (FIRST VERSION) • Howshouldweconditionalize?

  17. PROPOSAL (FIRST VERSION) • ForP1w(), therelevantevidenceisR(w). • ForP2w(P1()=r), therelevantevidenceisKR(w).

  18. CONDITIONALIZATION (FIRST VERSION) • C* rule: Fori 1: Piw(Pi-1(…P()=r...)) = Pprior(Pi-1(…P()=r…) | Ki-1...KR(w)) whereKi-1isthesameK-operatoriteratedi-1 times

  19. DIFFICULTIES • C* divorcesprobability 1 fromknowledge.

  20. A MODEL FOR MODERATE TRANSPARENCY (SECOND VERSION) • M= <W, R1,...,Rn..., Pprior, v> • New operatorsK0…Kn…, in additiontoP0, …Pn… • We define a sequence of relationsR1…RnwhichcorrespondtothedifferentKs. • TheRs are nested: RiRi-1 ...R1 • Riis a reflexive relation over W, for all i, and transitive for i> 1.

  21. A MODEL FOR MODERATE TRANSPARENCY • Ourconditionalization rule nowincorporatesoperatorsK1,… Kn… definedonthebasis of relationsR1,… Rn… • C** rule: Fori 1: Piw(Pi-1(…P()=r...)) = Pprior(Pi-1(…P()=r | Ki-1...KR(w)) where “Ki-1…KR(w)”includesi-1 higher-orderK-operators

  22. A MODEL FOR MODERATE TRANSPARENCY • Intendedinterpretation of theformalism: • “K2p” does not make sense! • A second-order evidential probability claim is the evidential probability of a probability statement. • Mutatis mutandis for higher-order levels and for conditional evidential probabilities.

  23. SOME CONSEQUENCES • WhyshouldwedemandsuchrequirementsfortheRs? They are notad hoc! • Higher-orderprobabilityrequiresincreasinglycomplexprobabilisticclaims. • Forsecond-orderevidentialprobability in w:  WeconditinalizeoverKR(w)  Thusthesecond-orderprobability of P1(R(w))is 1  ThustheagentknowsthatKR(w)  K2KR(w)shouldbe true in w

  24. SOME CONSEQUENCES • KK2KKK2 Principle • (if [K2KR(w)] isnotempty, foranyw) • (KK2K) KKPrinciple • (if [K2KR(w)] isnotempty, forsomew) • K2KK3K2KKK+Principle

  25. SOME CONSEQUENCES A restrictedversion of possitiveintrospection holds:  Quasi-transparencyprinciples • KK+, KKand KK2result from conditionalizing over higher-order levels of evidence and from the attempt to adjust probability language and knowledge attribution in a progressively coherent way.

  26. SOME CONSEQUENCES • Links betweenlower- and higher-orderprobabilities: • If P1w() = r = 1 or 0, then P2w(P1()=r) = 1. • If R1is an equivalence relation, P2w(P1()=r) is either 1 or 0. • Suppose P2w(P()=r) = s. If 0 r  1 and R1 is not transitive, then s need not be either 1 or 0.

  27. ON THE PROBABILISTIC REFLECTION PRINCIPLE (PRP) • PRP: P2w( | P1()=r) = r (for wW) • Iterated PRP: Piw( | Pi-1( | Pi-2(|…)….)=r) = r • IsPRP a theoreticaltruth of M?

  28. ON PROBABILISTIC REFLECTION • Necessary and sufficient condition for Iterated PRP Ri is an equivalence relation and Ri = Ri-1 iff for all wW and any L0: if Pi+1w(-|-) exists, then Pi+1w( | Pi( | Pi-1(|…)….) = r) = r

  29. RELATION TO OTHER WORK Paul Egré/ JérômeDokic • Principal motivation: todeactivateWilliamson’ssoriticargumentoninexactknowledge • Perceptual vs. reflectiveknowledge • (KK’) KKK • Transparencyfailures do notgeneralize

  30. RELATION TO OTHER WORK Differences • 1. Egré/ Dokic do notoffer a probabilisticframework. • 2. Theyfocusonreflectionover perceptual knowledge, exclusively. • 3. KK’ Principleisimposed “fromtheoutside”.  Thepresentmodelforquasi-transparency can beseen as a refinement and extension of someaspects of thesystemsuggestedbyEgré - Dokic.

  31. CONCLUSIONS • Once weclarifysome conceptual aspects of higher-orderprobabilities… • …weobtainthevindication of a number of introspectiveprinciples, orprinciples of quasi-transparency.

  32. CONCLUSIONS • Quasi-transparency principles were not just assumed to hold, but they have been obtained as a result of implementing a number of natural constraints on the structure of the system.  Formally speaking, they behave quite differently from presuppositions of consistency or deductive closure.

  33. CONCLUSIONS • Theframeworkvindicatestheintuitionthatfirst- and second-orderknowledgediffersubstantially: • Differentattitudesaboutignorance • Differentattitudestoward “margin of error” principles • Second-orderknowledgeisconcernedwiththe “ratification” of first-orderattitudes.

  34. CONCLUSIONS • Quasi-transparencyfullyvindicatesthenormative link betweenself-knowledge and responsibility.  K+Kp: “responsibleknowledge” of p.

  35. CONCLUSIONS  Second-orderknowledge, as a state of epistemicresponsibility, is a desideratumwehavequa agents.

  36. Thankyou!

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